Growing Problem Solvers provides four original, related, classroom-ready mathematical tasks, one for each grade band. Together, these tasks illustrate the trajectory of learners’ growth as problem solvers across their years of school mathematics.

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### Evthokia Stephanie Saclarides, Brette Garner, Gladys Krause, Claudia Bertolone-Smith, and Jen Munson

Learning to teach mathematics is a complex endeavor, requiring sustained focus and time. Yet time is especially scarce in elementary teacher education programs, where preservice teachers (PSTs) learn all content areas. Through a collaborative self-study, five teacher educators identified three time-related tensions in elementary mathematics methods courses: (a) teaching mathematics content and pedagogy; (b) connecting theory and practice; and (c) promoting social contexts in teaching mathematics. To address these tensions, we offer three design principles and illustrative examples: (a) addressing multiple goals for each course component; (b) developing PSTs’ dispositions over time; and (c) building on PSTs’ strengths to develop understanding of mathematics. We present a reflection tool to assist mathematics teacher educators in designing their courses to maximize their instructional time.

### Roger S. Wolbert

This department provides a space for current and past PK–12 teachers of mathematics to connect with other teachers of mathematics through their stories that lend personal and professional support.

### Enrique Ortiz

This article presents an example of discovering an idea through creative play. After some trial and error, I drew a wonderful image, which I later learned was a two-dimensional view of a four-dimensional shape called tesseract.

### Xiaobo She and Timothy Harrington

Get familiar with this visual instructional tool to help students make sense of mathematical relationships and select suitable operations for word problems at varied grade levels.

### Jared Webb and P. Holt Wilson

## ABSTRACT

In this article, we describe rehearsals designed for use in professional development (PD) with secondary mathematics teachers to support them in reimagining and refining their practice. We detail a theoretical framework for learning in PD that informs our rehearsal design. We then share evidence of secondary mathematics teachers’ improvements in classroom practice from a broader study examining their participation in a PD that featured the use of rehearsals and provide examples of the ways two teachers’ rehearsals of the practice of monitoring students’ engagement with mathematics corresponded to changes in their practice. We conclude with a set of considerations and revisions to our design and a discussion of the role of mathematics teacher educators in supporting teachers in expanding their practice toward more ambitious purposes for students’ mathematical learning.

### Jonee Wilson and Erin Smith

Instructional practices are often implemented in attempts to support multilingual learners. We discuss reasons that some of these well-intended practices may be problematic, and we share productive alternatives that we have observed in classrooms that effectively support multilingual learners.

### Corinne Thatcher Day

This hands-on task, featuring differentiation and open-ended learning, sets up students to discover area models for themselves. Organized around NCTM’s eight teaching practices from *Principles to Actions*, this article describes the task’s setup and implementation.

### Nicole Garcia, Meghan Shaughnessy, and D’Anna Pynes

Representing and recording student thinking in public spaces during mathematics discussions is challenging work. We share principles for recording student thinking in the moment and share an activity for improving your recording practice.

### Jennifer Ward and Victoria Damjanovic

This department provides a space for current and past PK–12 teachers of mathematics to connect with other teachers of mathematics through their stories that lend personal and professional support.